1 Answer

Siarhei Kavaleuski · Answer 1 · 2020-07-12T20:50:11+0000

For this case we have that by definition, the point-slope equation of a line is given by:

$y-y_ {0} = m (x-x_ {0})$

Where:

m: It's the slope

$(x_ {0}, y_ {0})$ : It is a point that belongs to the line

We find the slope with the given points:

$(x_ {1}, y_ {1}): (- 5,4)\\(x_ {2}, y_ {2}) :( 1,6)$

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {6-4} {1 - (- 5)} = \frac {2} {1 +5} = \frac {2} {6} = \frac {1} {3}$

Then, the equation is of the form:

$y-y_ {0} = \frac {1} {3} (x-x_ {0})$

We substitute the point
(1,6) :

$y-6 = \frac {1} {3} (x-1)$

Finally, the equation is:

$y-6 = \frac {1} {3} (x-1)$

Answer:

$y-6 = \frac {1} {3} (x-1)$

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